The Two-Weighted Inequalities for Sublinear Operators Generated by B Singular Integrals in Weighted Lebesgue Spaces

Abstract

In this paper, the authors establish several general theorems for the boundedness of sublinear operators (B sublinear operators) satisfies the condition (1.2), generated by B singular integrals on a weighted Lebesgue spaces \(L_{p,\omega,\gamma}(\mathbb{R}_{k,+}^{n})\), where \(B=\sum_{i=1}^{k} (\frac{\partial^{2}}{\partial x_{k}^{2}} + \frac{\gamma_{i}}{x_{i}}\frac{\partial}{\partial x_{i}} )\). The condition (1.2) are satisfied by many important operators in analysis, including B maximal operator and B singular integral operators. Sufficient conditions on weighted functions ω and ω1 are given so that B sublinear operators satisfies the condition (1.2) are bounded from \(L_{p,\omega,\gamma}(\mathbb{R}_{k,+}^{n})\) to \(L_{p,\omega_{1},\gamma}(\mathbb{R}_{k,+}^{n})\).